
in which \(\phi = \left\lbrace \phi _l,\phi _r,\phi _d\right\rbrace \) . In other words, the joint approximate posterior distribution is a product of prior and three single view posterior distributions called product of experts (PoE) [1]}. When these four distributions are all Gaussian which means \(p(\mathbf {z})=\mathcal {N}(\mu _0|\mathbf {\Sigma }_0)\) , \(\tilde{q}_{\phi _l}(\mathbf {z}|\mathbf {x}^l)=\mathcal {N}(\mu _l|\mathbf {\Sigma }_l)\) , \(\tilde{q}_{\phi _r}(\mathbf {z}|\mathbf {x}^r)=\mathcal {N}(\mu _r|\mathbf {\Sigma }_r)\)  and \(\tilde{q}_{\phi _d}(\mathbf {z}|\mathbf {x}^d)=\mathcal {N}(\mu _d|\mathbf {\Sigma }_d)\) , there is an analytical solution of the product distribution acquired above [2]}:
\(q_\phi (\mathbf {z}|\mathbf {x})=\mathcal {N}(\mu |\mathbf {\Sigma }),\) 
